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Moscow Mathematical Journal, 2003, Volume 3, Number 2, Pages 457–473
DOI: https://doi.org/10.17323/1609-4514-2003-3-2-457-473 (Mi mmj95) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator

G. Feldera, L. J. Stevensb, A. N. Varchenkob

a Departement für Mathematik, Eidgenösische Technische Hochschule Zürich
b Department of Mathematics, University of North Carolina at Chapel Hill
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DOI: https://doi.org/10.17323/1609-4514-2003-3-2-457-473
Abstract: We consider the space of elliptic hypergeometric functions of the $\mathfrak{sl}_2$ type associated with elliptic curves with one marked point. This space represents conformal blocks in the $\mathfrak{sl}_2$ WZW model of CFT. The modular group acts on this space. We give formulas for the matrices of the action in terms of values at roots of unity of Macdonald polynomials of the $\mathfrak{sl}_2$ type.
Key words and phrases: Elliptic hypergeometric functions, conformal blocks, Macdonald polynomials.
Received: October 2, 2002
Bibliographic databases:
MSC: Primary 39Axx; Secondary 11Fxx, 20Gxx, 32G34, 33Dxx.
Language: English
Citation: G. Felder, L. J. Stevens, A. N. Varchenko, “Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator”, Mosc. Math. J., 3:2 (2003), 457–473
Citation in format AMSBIB
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\by G.~Felder, L.~J.~Stevens, A.~N.~Varchenko
\paper Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator
\jour Mosc. Math.~J.
\yr 2003
\vol 3
\issue 2
\pages 457--473
\mathnet{http://mi.mathnet.ru/mmj95}
\crossref{https://doi.org/10.17323/1609-4514-2003-3-2-457-473}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2025269}
\zmath{https://zbmath.org/?q=an:1074.33014}
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